A BEM sensitivity and shape identification analysis for acoustic scattering in fluid-solid problems

Abstract

In this paper a boundary element formulation for the sensitivity analysis of structures immersed in an inviscide fluid and illuminated by harmonic incident plane waves is presented. Also presented is the sensitivity analysis coupled with an optimization procedure for analyses of flaw identification problems. The formulation developed utilizes the boundary integral equation of the Helmholtz equation for the external problem and the Cauchy-Navier equation for the internal elastic problem. The sensitivities are obtained by the implicit differentiation technique. Examples are presented to demonstrate the accuracy of the proposed formulations.1998 John Wiley & Sons, Ltd.

A BEM sensitivity formulation for three‐dimensional active noise control

“…The partial derivatives with respect to m (φ or θ or ψ) of the distance r can be evaluated as follows (23) r ,m = (r 2 j ) 1 /2 ,m = r j r j,m r where r j,m with j = 1 , 2 , 3 is the derivative of the component r j along the j-axes with respect to the design variable m. The derivative of r ,n with respect to m can be written as follows (24) r ,nm = ∂ ∂m ∂r ∂n = n j r j,m + n j,m r j − r ,n r ,m r where n j,m indicates the derivative of the outward normal n j along the j-axes with respect to the design variable m.…”

“…In order to evaluate (23) and (24), only the derivative with respect to the design variable of the node coordinates x j in the global coordinate system is required. It should be noted that r j,m coincides with x j,m when the element node belongs to the secondary source boundary, whereas it coincides with −x j,m when the point source is on the secondary surface.…”

“…The proposed method has been applied to accelerate both the assembly time of matrices H and G, and the post-processing step (aimed at calculating the potential of the internal points that constitute the CV) of matrices H and G. Furthermore, since the singularities of the kernels involved in the sensitivity problem are of the same order as the singularities of the kernels involved in the direct approach [24], the sensitivity matrices, H ,m and G ,m of equation (33) and H ,m and G ,m of equation (36), can all be evaluated using the proposed approach. It is worth noting that the programming effort for the application of the H-matrix ACA is the same for the two systems of equations (i.e., the direct system and the sensitivity system).…”

“…The proposed BEM is coupled with the Adaptive Cross Approximation (ACA), the Hierarchical matrix (H-matrix) format and the GMRES [21] to allow fast solutions for large scale problems. Previous work on BEM sensitivities can be found in [22][23][24][25][26][27][28].…”

Crack identification in two-dimensional unilateral contact mechanics with the boundary element method

“…Most published work concerns crack and cavity identi®cation in ®elds governed by Laplace equation (Friedman and Vogelius 1989;Nishimura and Kobayashi 1991;Santosa and Vogelius 1991;Zeng and Saigal 1992), elastostatic equation (Tanaka and Masuda 1986;Schnur and Zabaras 1992;Bezerra and Saigal 1993;Kassab et al 1994;Mellings and Aliabadi 1995;Tosaka et al 1995), Helmholtz and elastodynamic equations (Tanaka et al 1992;Kobayashi 1994;Nishimura and Kobayashi 1995;Burczyn Âski et al 1997;Mallardo and Aliabadi 1998). In all the papers dealing with elastostatics and elastodynamics the crack is treated as bilateral, thus the numerical results are not corresponding to the actual physical behaviour.…”